Question

Q5. If the CI on a certain sum for 2 years at 6% be Rs. 25.75, what would be the SI?
(a) Rs. 25
(b) Rs. 24
(c) Rs. 20
(d) Rs. 15
(e) None of these

Answer 1

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$\underline{ \tt \: given :}$

CI = 25.75

time, t = 2 yrs

rate of interest, r = 6%

principal, p = ?

As we know

$\boxed{ \bf ci = p( {1 + \frac{r}{100} )}^{t} - p}$

so,

$\bf 25.75 = p{(1 + \frac{6}{100}) }^{2} - p \\ \\ \bf 25.75 = p( {(1 + \frac{6}{100}) }^{2} - 1) \\ \\ \bf 25.75 = p(1 + \frac{36}{ {(100)}^{2} } + \frac{12}{100} - 1) \\ \\ \bf 25.75 = p( \cancel{1} + \frac{36}{ {(100)}^{2} } + \frac{12}{100} \: \cancel{ - 1}) \\ \\ \bf 25.75 = p( \frac{36 + 1200}{ {(100)}^{2} } ) \\ \\ \bf 25.75 = p( \frac{1236}{10000} ) \\ \\ \bf \: p = \frac{25.75 \times 10000}{1236} \\ \\ \boxed{ \bf \: p = 208.3}$

Now we know the formula for

simple interest si

$\boxed{ \tt{si = \frac{p \times r \times t}{100} }}$

$\bf \: si = \frac{208.3 \times 6 \times 2}{100} \\ \\ \bf \: si = \frac{2499.6}{100} \\ \\ \boxed{ \bf \: si = 24.996}$

SI calculated is approximately equal to

SI = Rs 25

So,

Correct option should be

(a) Rs. 25